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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 2, Pages 224–255
DOI: https://doi.org/10.7868/S0044466914020057 (Mi zvmmf9989) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Algorithms for computing Minkowski operators and their application in differential games

P. E. Dvurechensky, G. E. Ivanov

Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
Full-text PDF (503 kB) Citations (17)
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DOI: https://doi.org/10.7868/S0044466914020057
Abstract: The Minkowski operators are considered, which extend the concepts of the Minkowski sum and difference to the case where one of the summands depends on an element of the other term. The properties of these operators are examined. Convolution methods of computer geometry and algorithms for computing the values of the Minkowski operators are developed. These algorithms are used to construct epsilon-optimal control strategies in a nonlinear differential game with a nonconvex target set. The errors of the proposed algorithms are estimated in detail. Numerical results for the conflicting control of a nonlinear pendulum are presented.
Key words: Minkowski sum and difference, Minkowski operator, differential game, optimal control strategy, computational algorithms, errors of algorithms.
Received: 26.06.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 2, Pages 235–264
DOI: https://doi.org/10.1134/S0965542514020055
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: P. E. Dvurechensky, G. E. Ivanov, “Algorithms for computing Minkowski operators and their application in differential games”, Zh. Vychisl. Mat. Mat. Fiz., 54:2 (2014), 224–255; Comput. Math. Math. Phys., 54:2 (2014), 235–264
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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